This paper uses thin-film asymptotics to show how a thin vapour layer can support
a liquid which is heated from below and cooled from above, a process known as
horizontal film boiling. This approach leads to a single, strongly-nonlinear evolution
equation which incorporates buoyancy, capillary and evaporative effects. The stability
of the vapour layer is analysed using a variety of methods for both saturated and
subcooled film boiling. In subcooled film boiling, there is a stationary solution, a
constant-thickness vapour film, which is determined by a simple heat-conduction
balance. This is Rayleigh–Taylor unstable because the heavier liquid is above the
vapour, but the instability is completely suppressed for sufficient subcooling. A
bifurcation analysis determines a supercritical branch of stable, spatially-periodic
solutions when the basic state is no longer stable. Numerical branch tracing extends
this into the strongly-nonlinear regime, revealing a hysteresis loop and a secondary
bifurcation to a branch of travelling waves which are stable under certain conditions.
There are no stationary solutions in saturated film boiling, but the initial development
of vapour bubbles is determined by directly solving the time-dependent evolution
equation. This yields important information about the transient heat transfer during
bubble development.
Theta functions, Gaussian series, and spatially periodic solutions of the Korteweg–de Vries equation
